Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible euler equations

doi:10.1007/s00332-006-0800-3

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	Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible euler equations
	Hou, Thomas Y.; Li, Ruo
	2006-12-01
发表期刊	JOURNAL OF NONLINEAR SCIENCE
ISSN	0938-8974
卷号	16 期号:6 页码:639-664
摘要	We study the interplay between the local geometric properties and the non-blowup of the 3D incompressible Euler equations. We consider the interaction of two perturbed antiparallel vortex tubes using Kerr's initial condition [15] [Phys. Fluids 5 (1993), 1725]. We use a pseudo-spectral method with resolution up to 1536 x 1024 x 3072 to resolve the nearly singular behavior of the Euler equations. Our numerical results demonstrate that the maximum vorticity does not grow faster than doubly exponential in time, up to t = 19, beyond the singularity time t = 18.7 predicted by Kerr's computations [15], [18]. The velocity, the enstrophy, and the enstrophy production rate remain bounded throughout the computations. As the flow evolves, the vortex tubes are flattened severely and turned into thin vortex sheets, which roll up subsequently. The vortex lines near the region of the maximum vorticity are relatively straight. This local geometric regularity of vortex lines seems to be responsible for the dynamic depletion of vortex stretching.
DOI	10.1007/s00332-006-0800-3
语种	英语
WOS研究方向	Mathematics ; Mechanics ; Physics
WOS类目	Mathematics, Applied ; Mechanics ; Physics, Mathematical
WOS记录号	WOS:000241890200004
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3207
专题	中国科学院数学与系统科学研究院
通讯作者	Hou, Thomas Y.
作者单位	1.CALTECH, Pasadena, CA 91125 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100080, Peoples R China 3.Peking Univ, LMAM, Beijing 100871, Peoples R China 4.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Hou, Thomas Y.,Li, Ruo. Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible euler equations[J]. JOURNAL OF NONLINEAR SCIENCE,2006,16(6):639-664.
APA	Hou, Thomas Y.,&Li, Ruo.(2006).Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible euler equations.JOURNAL OF NONLINEAR SCIENCE,16(6),639-664.
MLA	Hou, Thomas Y.,et al."Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible euler equations".JOURNAL OF NONLINEAR SCIENCE 16.6(2006):639-664.